Problem: Simplify the following expression: $ q = \dfrac{-5r - 4}{-4r} - \dfrac{-1}{4} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-5r - 4}{-4r} \times \dfrac{4}{4} = \dfrac{-20r - 16}{-16r} $ Multiply the second expression by $\dfrac{-4r}{-4r}$ $ \dfrac{-1}{4} \times \dfrac{-4r}{-4r} = \dfrac{4r}{-16r} $ Therefore $ q = \dfrac{-20r - 16}{-16r} - \dfrac{4r}{-16r} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-20r - 16 - 4r }{-16r} $ Distribute the negative sign: $q = \dfrac{-20r - 16 - 4r}{-16r}$ $q = \dfrac{-24r - 16}{-16r}$ Simplify the expression by dividing the numerator and denominator by -8: $q = \dfrac{3r + 2}{2r}$